Ken Livingstone said last night Ian Tomlinson appeared to have been assaulted by a police officer who should be suspended from duty and treated in the same way as violent protesters at the G20 demonstration.

As all the main political parties expressed horror at the images of the newspaper vendor's final moments - and united in calling for a speedy inquiry - the former London mayor warned that police could face manslaughter charges.

In his first comments about the death of Tomlinson, Livingstone told Radio 4's PM programme: "It [the video] is disturbing. It might be that the officer had been provoked by others, lost control of his temper, whatever. But if there is a link to the death then clearly there is a potential manslaughter charge."

Livingstone said he was concerned about the attitude among some police officers to the G20 demonstrations. "What worried me in the build-up to this is that some of the demonstrators were saying stupid things like 'if the police want violence they can have it'. But whereas in previous years the police would try and calm that down you had police officers saying 'we're up for it'.

"If that sort of thinking permeates through the lower ranks and some of the demonstrators are being excessive and spitting then somebody may lose control. And that may be what happened here. It does look like an assault. I have seen a lot of the coverage and talked to people who were there who talked about how good natured a lot of the police were and how good natured a lot of the demonstrators were. But ... there were some violent police and some violent demonstrators. Our job should be to get them all and not to treat them differently."

Boris Johnson, the London mayor, told Radio 4's The World At One: "I have seen the footage like millions of other people and of course I find it very disturbing. It seems to be a very disturbing series of images." But he refused to prejudge the investigation by the IPCC.

The main political parties agreed on the need for a quick inquiry by the IPCC which could lead to a criminal investigation. Jacqui Smith, the home secretary, said: "I'm glad that the IPCC themselves called for further evidence in order to be able to do that inquiry as quickly as possible. If it identifies the need for a criminal investigation then that also needs to be pursued."

Chris Grayling, the shadow home secretary, said: "These latest revelations are extremely alarming and leave big questions to be answered by the police. It is right that there should be an independent investigation." David Howarth, the Liberal Democrat justice spokesman, said: "This video clearly shows an unprovoked attack by a police officer on a passerby. It is sickening. There must be a full-scale criminal investigation."

Shami Chakrabarti, of the human rights organisation Liberty, said: "Clear images of an armoured policeman assaulting an innocent bystander from behind impugn the whole attitude to policing protests by the Metropolitan police. The IPCC failed its first major test in the [Jean Charles de] Menezes case. If the commission is to regain a shred of public confidence it must do far better in terms of speed, sanction and transparency."